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John L.
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Christofides algorithm (by hand)

I am following this algorithm example: https://en.wikipedia.org/wiki/Christofides_algorithm#example

The graph:

enter image description here

Calculate minimum spanning tree T:

enter image description here

Calculate the set of vertices O with odd degree in T

Same as "the minimum spanning tree T" as the degree of all vertices are odd.

Form the subgraph of G using only the vertices of O

(as all were odd, this should give us the original graph) enter image description here

Construct a minimum-weight perfect matching M in this subgraph

(I am not sure if I did this right) enter image description here

Unite matching and spanning tree T ∪ M to form an Eulerian multigraph

enter image description here

This is definitely not right.

What went wrong?